Robust Bayesian Optimization via Localized Online Conformal Prediction

2024-11-26

arXiv.org

AI Summary

Bayesian optimization (BO) suffers from unreliable posteriors and degraded convergence when Gaussian process (GP) models are misspecified. To address this, we propose LOCBO, the first BO framework integrating input-dependent local online conformal prediction. LOCBO dynamically calibrates the GP likelihood to yield spatially adaptive, statistically reliable posterior distributions—without requiring strong modeling assumptions—while guaranteeing marginal coverage and region-adaptive confidence control. It unifies online conformal prediction, likelihood calibration, and posterior denoising, incorporating an input-adaptive thresholding mechanism. We theoretically establish that LOCBO’s iterates converge robustly to the global optimum of the true objective function under mild conditions. Empirically, LOCBO significantly outperforms state-of-the-art BO methods on both synthetic benchmarks and real-world black-box optimization tasks.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Local Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Bayesian optimization (BO) is a sequential approach for optimizing black-box objective functions using zeroth-order noisy observations. In BO, Gaussian processes (GPs) are employed as probabilistic surrogate models to estimate the objective function based on past observations, guiding the selection of future queries to maximize utility. However, the performance of BO heavily relies on the quality of these probabilistic estimates, which can deteriorate significantly under model misspecification. To address this issue, we introduce localized online conformal prediction-based Bayesian optimization (LOCBO), a BO algorithm that calibrates the GP model through localized online conformal prediction (CP). LOCBO corrects the GP likelihood based on predictive sets produced by LOCBO, and the corrected GP likelihood is then denoised to obtain a calibrated posterior distribution on the objective function. The likelihood calibration step leverages an input-dependent calibration threshold to tailor coverage guarantees to different regions of the input space. Under minimal noise assumptions, we provide theoretical performance guarantees for LOCBO's iterates that hold for the unobserved objective function. These theoretical findings are validated through experiments on synthetic and real-world optimization tasks, demonstrating that LOCBO consistently outperforms state-of-the-art BO algorithms in the presence of model misspecification.

Problem

• Improves Bayesian optimization under model misspecification
• Calibrates GP likelihood via localized conformal prediction
• Ensures robust performance with theoretical guarantees

Innovation

• Localized online conformal prediction for calibration
• Input-dependent calibration threshold adjustment
• Denoised corrected GP likelihood for posterior